# Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions

Variable
Term
Operation
Expression
Evaluate
Substitute

## Lesson

A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are $a$ , $x$ , $y$ , $\theta$  and $\lambda$ . The letters x and y are commonly used, but remember that any other symbols would work just as well.

Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.

Some examples of variables in use:

• $3x$  -- three times of $x$ .
• $5-y$  -- five minus $y$
• $2\div s$  or ${\frac {2}{s}}$ -- 2 divided by $s$

A term is a number or a variable or a cluster of numbers and variables multiplied and or divided separated by addition and subtraction.

Examples of terms:

• $3+5$  The terms are 3 and 5.
• ${\frac {6}{x}}$  The term is $6/x$ , 6 over $x$  is one term, because the operation is division.
• $6x+5$  The terms are 6$x$  and 5, 6$x$  and 5 are separate terms because they are separated by a addition or subtraction.

An operation is a thing you do to numbers, like add, subtract, multiply, or divide. You use signs like +, , *, or / for operations.

An expression is two or more terms, with operations between all terms.

Examples of expressions:

• $3\div 6$
• $8\times x$
• $x\times 6+y$
• $a\times b\times c\times d$

To evaluate an expression, you do the operations to the terms of an expression.

Examples of evaluating expressions:

• $3+4$  evaluates to 7.
• $18\div 3$  evaluates to 6.
• $4\times 5-3$  evaluates to 17.

To evaluate an expression with variables, you substitute (put a thing in the place of an other thing) numbers for the variables.

Examples of substituting: (Substitute 3 for x in these examples.)

• $x+4$  is $3+4$ .
• $18\div x$  is $18\div 3$ .
• $4\times 5-x$  is $4\times 5-3$ .

## Example Problems

Evaluate the following expressions

 $5\times x$ When $x=2$ $5\times 2$ Substitute 2 for $x$ . $10$ Evaluate $5\times 2$ to get the answer.
 ${\frac {x}{3}}+y$ When $x=9$ and $y=4$ ${\frac {9}{3}}+4$ Substitute 9 for $x$ and substitute 4 for $y$ . $7$ Evaluate ${\frac {9}{3}}+4$ to get the answer.

## Practice Problems

remember order of operations

Evaluate each expression if $a$  = 1, $b$  = 2, $c$  = 3, and $d$  = 5.

1

 $5\times b=$ 2

 $9\times c=$ 3

 $c-2=$ 4

 $d-5=$ 5

 ${\frac {b}{2}}=$ 6

 ${\frac {36}{c}}=$ 7

 $b\times c+2=$ 8

 $b\times c\times d-5=$ Evaluate each expression if $x$  = 4, $y$  = 2, and $z$  = 3.

9

 $x+y=$ 10

 $2z=$ 11

 $xz=$ 12

 $x+y+z=$ 13

 $xy+z=$ 14

 $yz-x=$ 15

 ${\frac {6}{y}}+z=$ 16

 ${\frac {2x}{2+y}}=$ More harder questions: Evaluate each expression if $x$  = 5, $y$  = 8, and $z$  = 9.

17

 $(2+x)\times y=$ 18

 ${\frac {3y-9}{5}}=$ 19

 ${\frac {27}{x+4}}-(y-5)=$ 20

 ${\frac {z+12}{2x-3}}+y=$ 21

 $\left({\frac {6x}{2+y}}-z\right)+\left(x-{\frac {z}{3}}\right)=$ « Basic AlgebraVariables and Expressions » Order of Operations Working With Negative Numbers